I'm working on an answer now; and it's not one rule -- it's several, interacting.
–
John LawlerJun 27 '14 at 15:36

@JohnLawler Isn't it simply that not is more closely associated with the main, rather than the auxiliary, verb and is kept proximal when question form shifts subject order?
–
bibJun 27 '14 at 15:46

1

You could look at it that way, but measuring the degree of association between a negative and a verb is hard to do accurately. This is a syntactic phenomenon, and semantic descriptions are usually not helpful.
–
John LawlerJun 27 '14 at 15:55

Not only is there an uncontracted sentence available for every contracted one, but there is a statement (ideally, the answer) for every question; contractions as such are just one part of question formation. Presumably the first pair of sentences above are possible answers to the second pair, right?

In fact, the second question, while grammatical, has a very stilted feel to it, like it was spoken by somebody wearing pince-nez spectacles. In a word, it's overly formal; technically, one would say it is high-register syntax in a colloquial exchange, and it gets marked as strange.
So mostly English speakers don't say things like Did you not check your voicemail?

What's going on is the mechanics of Question Formation, which consists of two steps,
in the simplest case of a yes-no question.

Start with a declarative sentence, e.g, He has checked his voicemail.

Invert the subject noun phrase and the first auxiliary verb: Has he checked his voicemail?

There are two caveant here:
(1) be is always an auxiliary verb, even if it's the only verb in the sentence
(2) if there isn't any auxiliary verb, invoke Do-Support

In the case of auxiliary verb-negative contractions, as noted, they are optional in the basic sentence.
Either hasn't or has not will work (though again, they would be used in different contexts)

He hasn't checked his voicemail ~ He has not checked his voicemail.

If we apply Question formation to both of these, we get, respectively,

Hasn't he checked his voicemail? ~ Has he not checked his voicemail?

That's why Did not you ..? is ungrammatical -- it's not a possible output of Question Formation.
As it says in the link, contractions are only optional in their original position.
If they're moved, they're frozen, as single words, and can't be expanded again.

Maybe this is more Latin language and usage, but can you elaborate on why you pluralized caveat to caveant?
–
Two-Bit AlchemistJun 27 '14 at 21:08

1

There are more complications with the verb to have: "I haven't a clue." / "I haven't a cent." but for most native speakers *"I haven't a dog." "Haven't you a quid to spare?" might be acceptable but I think the same with "dollar" wouldn't be (being from the other side of the ocean). I was taught that "I haven't got" is vulgar but not everyone prefers "I don't have". "I have not" is still acceptable in some registers. I suppose that the set phrases point to a recent syntactic change.
–
riciJun 27 '14 at 23:26

1

@rici: That's because the have that means 'possess' is not an auxiliary verb, at least in the U.S. In the U.K, it can count as auxiliary or not, depending on dialect.
–
John LawlerJun 27 '14 at 23:27

1

@Two-BitAlchemist In English, caveat (warning) is a noun whose plural is caveats. In Latin, caveat (let him/her beware) is the 3rd person singular present subjunctive form of the verb cavere (to beware), and the plural in Latin is caveant (let them beware). Unfortunately, pluralizing the verb in Latin does not have the same meaning as pluralizing the noun in English. Pluralizing the verb indicates one warning directed to multiple recipients, while pluralizing the noun signifies more than one warning.
–
DanielJun 28 '14 at 2:03

The answer is really quite simple. The issue here is the difference between the statement form, and the question form. If the first instance provided by the OP was also a question, it would be written, "Why did I not check my email?", because the question is creating by inverting the subject and verb.

Some thoughts.....The world is full of contradictions, illogicalities and paradoxes. To assume that those that occur in language are of any particular significance is surely erroneous. Behind these observations lies a yearning for a linguistic rule that will identify correct, or incorrect, usage, in all circumstances, if only we could find it, but for every example of a rule there seems to be an exception, and for every exception there seems to be another rule. This pursuit of conformity has its origins elsewhere, outside language. However there are rules, but you won't find them in any standard text, but you might find them in the history of language. If you want to trace this history you will have trouble getting beyond Latin and Greek, but it is in the Hebrew that you will find many of the answers to the questions above. As a general rule of thumb you cannot make an error in your first language, which you learned in your developmental years, but you can in your second or subsequent languages, learned after the development years are over...... The only test, surely, is a semantic one.....